The hidden-charm pentaquark and tetraquark states have been a topic of significant interest in particle physics, particularly in the context of charmonium-like states and hidden-charm multiquark systems. Over the past decade, numerous charmonium-like states have been observed experimentally, including charged $ Z_c $ states and bottomonium-like $ Z_b $ states, which cannot be explained by the traditional quark model. These states are considered potential candidates for hidden-charm tetraquark or molecule states composed of charmed mesons. Recently, the LHCb Collaboration discovered two hidden-charm pentaquark states, which are also beyond the quark model. This review summarizes the current experimental progress and theoretical interpretations of these multiquark states. The charmonium-like XYZ states, including $ X(3872) $, $ Y(3940) $, $ Y(4140) $, $ Y(4274) $, and $ Z^{+}(4430) $, have been observed through various production mechanisms such as B meson decays, initial state radiation, double charmonium production, and two-photon fusion. These states exhibit exotic quantum numbers and have been interpreted as either molecular states or tetraquark states. Theoretical models such as the molecular scheme, meson exchange model, and QCD sum rules have been used to explain these states. The hidden-charm pentaquark states observed by LHCb are also discussed, with their quantum numbers and decay patterns analyzed. Theoretical interpretations of these states include the molecular scheme, where they are considered as loosely bound states of two heavy mesons, and the tetraquark scheme, where they are composed of two quarks and two antiquarks. The QCD sum rules and chiral quark model have also been applied to study these states. The kinematical effects and production and decay patterns of these states are discussed, along with their potential as hidden-bottom and doubly heavy pentaquark states. The review also addresses the challenges and puzzles in the theoretical models, such as the overpopulation of the quark model spectrum and the need for new theoretical frameworks to explain the observed states. Future measurements and experimental confirmations are discussed, as well as the connections between different XYZ states and the role of non-resonant schemes in their interpretation. The review concludes with an outlook on the future of hidden-charm multiquark states and their significance in understanding the non-perturbative behavior of QCD.The hidden-charm pentaquark and tetraquark states have been a topic of significant interest in particle physics, particularly in the context of charmonium-like states and hidden-charm multiquark systems. Over the past decade, numerous charmonium-like states have been observed experimentally, including charged $ Z_c $ states and bottomonium-like $ Z_b $ states, which cannot be explained by the traditional quark model. These states are considered potential candidates for hidden-charm tetraquark or molecule states composed of charmed mesons. Recently, the LHCb Collaboration discovered two hidden-charm pentaquark states, which are also beyond the quark model. This review summarizes the current experimental progress and theoretical interpretations of these multiquark states. The charmonium-like XYZ states, including $ X(3872) $, $ Y(3940) $, $ Y(4140) $, $ Y(4274) $, and $ Z^{+}(4430) $, have been observed through various production mechanisms such as B meson decays, initial state radiation, double charmonium production, and two-photon fusion. These states exhibit exotic quantum numbers and have been interpreted as either molecular states or tetraquark states. Theoretical models such as the molecular scheme, meson exchange model, and QCD sum rules have been used to explain these states. The hidden-charm pentaquark states observed by LHCb are also discussed, with their quantum numbers and decay patterns analyzed. Theoretical interpretations of these states include the molecular scheme, where they are considered as loosely bound states of two heavy mesons, and the tetraquark scheme, where they are composed of two quarks and two antiquarks. The QCD sum rules and chiral quark model have also been applied to study these states. The kinematical effects and production and decay patterns of these states are discussed, along with their potential as hidden-bottom and doubly heavy pentaquark states. The review also addresses the challenges and puzzles in the theoretical models, such as the overpopulation of the quark model spectrum and the need for new theoretical frameworks to explain the observed states. Future measurements and experimental confirmations are discussed, as well as the connections between different XYZ states and the role of non-resonant schemes in their interpretation. The review concludes with an outlook on the future of hidden-charm multiquark states and their significance in understanding the non-perturbative behavior of QCD.